Optimization of Train Planning for General Tree-Type Line

doi:10.12141/j.issn.1000-565X.220140

Abstract

Abstract:

In the background of rail transit network operation, the simple line and routing forms can no longer meet the diverse passenger travel demand. Therefore, in order to cope with the mismatch between traffic supply and demand brought about by passenger trips in complex directions, the paper proposed a rail transit line form of general Tree-type line based on the existing research on Y-type lines, and it was divided into diameter type and radius type with reference to the actual operating line cases. Firstly, the paper designed a line topology form of Tree-type line and established a multi-routing planning optimization model for Tree-type line by considering the distribution of passengers among different trains and taking the departure frequency as the decision variable and the passenger travel time and minimum operating cost as the target function. Then it designed and solved the non-dominant ranking genetic algorithm (NSGA-Ⅱ) with the elite strategy. The model and algorithm were validated using the RER A line in Paris as an example. Finally, the optimization scheme was compared with the split-line scheme. The results show that: the algorithm can find the Pareto frontier solutions of the train planning, and the travel time of passengers and the operation cost of enterprises show a significant negative correlation; the obtained optimization scheme has a significant reduction in the travel time of passengers and the operation cost of enterprises compared with the split-line scheme. It reduces the waiting time of passengers by 1.76% to 12.90%, the transfer time of passengers by 33.63% to 34.98%, the total running kilometres of trains by 7.69% to 21.67%, and the the number of trains on the line by 9 to 19.

Key words: urban rail transit, Tree-type line, train planning, NSGA-Ⅱ, travel time, operation cost

CLC Number:

U292.42

WEI Runbin, JIA Shunping, TONG Ruiyong, et al. Optimization of Train Planning for General Tree-Type Line[J]. Journal of South China University of Technology(Natural Science Edition), 2022, 50(11): 44-51.

Figures/Tables 10

Table 1

Fig.1

Fig.2

Table 2

Parameters and variables"

参数或变量	含义
$i, j$	分别代表树型线两端的分支
$n$	车站，车站 $n$ 与 $n + 1$ 之间为区间 $n$
$z$	按线路拓扑结构划分的区段
$Z$	区段 $z$ 的集合
$N 1$ ， $N 2$ ，…	分别代表图2中所示的车站
$Z Ⅰ$ ， $Z Ⅱ$ ，…	分别代表图2中所示的区段
$l n$ /m	车站 $n$ 与 $n + 1$ 之间的距离
$L i, j$ /m	交路 $i, j$ 的长度
$Q O D$	OD矩阵
$q o, d$	从 $o$ 站到 $d$ 站的客流
$v i, j$ /（m·s^-1）	交路 $i, j$ 的列车平均旅行速度
$θ$ /min	一次折返时间
$μ$ /min	一次换乘时间
$f i, j$	分支 $i$ 与分支 $j$ 之间往返的交路（即交路 $i, j$ ）列车的发车频率，决策变量
$f m i n$	最小发车频率
$f m a x$	最大发车频率
$C$	列车定员，人
$p n u p$ ， $p n d o w n$	分别代表上/下行的区间 $n$ 的断面客流
$η n u p$ ， $η n d o w n$	分别代表上/下行的区间 $n$ 的满载率
$η m a x$	最大满载率
$T$ /h	乘客总出行时间
$T 1, z$ /h	区段 $z$ 的乘客总候车时间
$T 2, z$ /h	区段 $z$ 的乘客总换乘时间
$S$ /元	企业运营成本
$S 1$ /元	车辆运营成本
$S 2$ /元	车辆使用成本
$α$ /（元?km^-1）	每列列车每公里运营费用
$β$ /（元?h^-1）	每列列车单位时间的折旧费

Table 2

Fig.3

Fig.4

Fig.5

Fig.6

Table 3

Optimization schemes"

类别	$f 1,4$	$f 1,5$	$f 2,4$	$f 2,5$	$f 3,4$	$f 3,5$	乘客出行时间/h	企业运营成本/元
优化方案1	8	4	6	0	0	12	12 834.62	130 158.00
优化方案2	8	4	2	5	4	7	12 885.40	127 783.20
优化方案3	6	6	3	4	5	6	12 894.98	127 094.40
优化方案4	2	9	2	4	10	3	12 962.15	121 336.80
优化方案5	0	10	3	4	11	2	13 016.11	119 383.20
优化方案6	0	10	2	4	12	2	13 076.20	118 026.00
优化方案7	0	10	2	4	10	2	13 768.52	113 402.40
优化方案8	0	10	0	6	11	1	13 888.28	113 197.80
优化方案9	0	10	2	4	9	2	14 210.24	110 802.60

Table 3

Table 4

References 17

1	姚恩建，张金萌，郇宁．效率与公平导向下城轨大小交路开行方案优化［J］．华南理工大学学报（自然科学版），2020，48（5）：41-48，57.
	YAO Enjian， ZHANG Jinmeng， HUAN Ning ．Equality-efficiency balance-oriented optimization of long-short route strategy in urban rail transit［J］．Journal of South China University of Technology （Natural Science Edition），2020，48（5）：41-48，57.
2	谭丽，韦子文．基于CCLPSO算法的Y型交路列车开行方案优化研究［J］．铁道科学与工程学报，2019，16（8）：2122-2129.
	TAN Li， WEI Ziwen ．Optimization research of train schedule of Y-type train routing mode based on CCLPSO algorithm［J］．Journal of Railway Science and Engineering，2019，16（8）：2122-2129.
3	梁青槐，柴树山，邓京维．区域轨道交通跨线运行行车密度优化模型［J］．北京交通大学学报，2020，44（1）：20-26.
	LIANG Qinghuai， CHAI Shushan， DENG Jingwei ．Optimization model of train operation density for cross-line in regional rail transit［J］．Journal of Beijing Jiaotong University，2020，44（1）：20-26.
4	ZHAO X， SUN Q， ZHU Y，et al ．Multi-routing planning design of Y-type urban rail transit［J］．Advances in Mechanical Engineering，2016，8（8）：1687814016667385.
5	RIEJOS F A O， BARRENA E， ORTIZ J D C，et al ．Analyzing the theoretical capacity of railway networks with a radial-backbone topology［J］．Transportation Research Part A：Policy and Practice，2016，84：83-92.
6	FIOOLE P J， KROON L， MARÓTI G，et al ．A rolling stock circulation model for combining and splitting of passenger trains［J］．European Journal of Operational Research，2006，174（2）：1281-1297.
7	江志彬，徐瑞华，吴强，等．多交路共线运行的城市轨道交通车辆运用优化［J］．同济大学学报（自然科学版），2014，42（9）：1333-1339，1431.
	JIANG Zhibin， XU Ruihua， WU Qiang，et al ．Optimal model for using of transit unit based on shared-path rail transit route［J］．Journal of Tongji University （Natural Science），2014，42（9）：1333-1339，1431.
8	郭建民，韩林飞，周建国，等．Y形共线模式下轨道交通列车开行方案研究［J］．铁道工程学报，2017，34（2）：87-92.
	GUO Jianmin， HAN Linfei， ZHOU Jianguo，et al ．Research on the operation scheme for rail transit with the Y-shaped collinear mode［J］．Journal of Railway Engineering Society，2017，34（2）：87-92.
9	李得伟，刘宗杰，王晓全，等．考虑乘客选择行为的城轨Y型线交路计划编制［J］．中国铁道科学，2018，39（4）：114-122.
	LI Dewei， LIU Zongjie， WANG Xiaoquan，et al ．Routing plan for Y-type line of urban rail transit considering passenger choice behavior［J］．China Railway Science，2018，39（4）：114-122.
10	LIU Y， HAN B ．Study on train routing plan of Y-line of urban rail transit considering passenger travel purpose［C］∥ Proceedings of the 2019 International Conference on Intelligent Transportation and Vehicle Engineering．Harbin：IOP Publishing，2020：1-11.
11	YANG A， WANG B， HUANG J，et al ．Service replanning in urban rail transit networks：cross-line express trains for reducing the number of passenger transfers and travel time［J］．Transportation Research Part C：Emerging Technologies，2020，115：102629.
12	杨安安，汪波，陈艳艳，等．基于能力影响的城市轨道交通跨线列车开行方案研究［J］．交通运输系统工程与信息，2017，17（6）：221-227.
	YANG Anan， WANG Bo， CHEN Yanyan，et al ．Plan of cross-line train in urban rail transit based on the capacity influence［J］．Journal of Transportation Systems Engineering and Information Technology，2017，17（6）：221-227.
13	ZHOU Y， YANG H， WANG Y，et al ．Integrated line configuration and frequency determination with passenger path assignment in urban rail transit networks［J］．Transportation Research Part B：Methodological，2021，145：134-151.
14	WEN J， LEURENT F， XIE X ．A transit bottleneck model for optimal control strategies and its use in traffic assignment in Paris［J］．Transportation Research Procedia，2017，22：65-74.
15	李得伟，李若怡，兰贞．巴黎RER线现状分析及对我国市域轨道交通发展的启示［J］．都市快轨交通，2017，30（5）：134-139.
	LI Dewei， LI Ruoyi， LAN Zhen ．Introduction of RER line in Paris and enlightenment to the development of regional rail transit in China［J］．Urban Rapid Rail Transit，2017，30（5）：134-139.
16	白广争，郭进，石红国，等．网络化城市轨道交通时刻表换乘协调优化研究［J］．铁道学报，2016，38（6）：1-7.
	BAI Guangzheng， GUO Jin， SHI Hongguo，et al ．Optimization for transfer coordination of network timetable in urban rail transit［J］．Journal of the China Railway Society，2016，38（6）：1-7.
17	许得杰，巩亮，朱宁，等．城市轨道交通多交路共线运营客流分配方法［J］．交通运输系统工程与信息，2021，21（5）：206-213.
	XU Dejie， GONG Liang， ZHU Ning，et al ．Passenger flow assignment method for common-line operation with multi-routing of urban rail transit［J］．Journal of Transportation Systems Engineering and Information Technology，2021，21（5）：206-213.

作者	年份	目标函数	决策变量	停站方案	编组方案
江志彬等^［7］	2014	上线车底数最小；折返时间最小	交路开行列车比例	站站停	固定编组
Zhao等^［4］	2016	乘客出行时间最小；列车走行公里最小	交路方案发车频率	站站停	固定编组
郭建民等^［8］	2017	乘客候车时间最小；列车走行公里最小；上线车底数最小	交路方案发车频率	站站停	固定编组
李得伟等^［9］	2018	乘客出行时间最小；列车走行公里最小；上线车底数最小	交路方案发车频率	站站停	固定编组
谭丽等^［2］	2019	乘客出行时间最小；列车走行公里最小；上线车底数最小	交路方案发车频率	站站停	固定编组
Liu等^［10］	2020	列车购置成本最小；列车走行公里最小；乘客出行成本最小	交路方案发车频率	站站停	固定编组
Yang等^［11］	2020	节省乘客出行时间最大；节省企业运营成本最大	交路方案发车频率	快慢车	固定编组

类别	乘客候车时间/h	乘客换乘时间/h	列车总走行里程/km	上线车底数
分线方案	11 892.28	3 808.67	3 930.60	83
优化方案1	10 358.11	2 476.51	3 628.20	74
优化方案3	10 388.50	2 506.48	3 526.08	74
优化方案4	10 440.42	2 521.73	3 362.96	71
优化方案6	10 547.67	2 528.53	3 281.40	68
优化方案7	11 240.41	2 528.10	3 146.48	66
优化方案9	11 682.41	2 527.83	3 079.02	64

[1]	ZHENG Yajing, MA Zihan, CHANG Xiaoting, et al. Comprehensive Optimization of Track Scale Configuration of Intermediate Station and Train Timetable of High-Speed Railway [J]. Journal of South China University of Technology(Natural Science Edition), 2023, 51(4): 115-123.
[2]	XU Zhihang, YAO Xinpeng, XU Zhigang, et al. Review of Research on Road Traffic Detectors and Its Optimized Deployment Methods [J]. Journal of South China University of Technology(Natural Science Edition), 2023, 51(10): 68-88.
[3]	LIN Peiqun XIA Yu ZHOU Chuhao. Freeway Travel Time Prediction Based on Spatial and Temporal Characteristics of Road Networks [J]. Journal of South China University of Technology(Natural Science Edition), 2021, 49(8): 1-11.
[4]	LIU Hanwu, LEI Yulong, FU Yao, et al. Adaptive Regenerative Braking Control Strategy of Range-Extended Electric Vehicle Based on Multi-Objective Optimization [J]. Journal of South China University of Technology (Natural Science Edition), 2021, 49(7): 42-50,65.
[5]	YAO Enjian ZHANG Jinmeng HUAN Ning. Equality-Efficiency Balance-Oriented Optimization of Long-Short Route Strategy in Urban Rail Transit [J]. Journal of South China University of Technology (Natural Science Edition), 2020, 48(5): 41-48,57.
[6]	ZHAO Lei GUAN Hongzhi ZHANG Xinjie ZHAO Pengfei WANG Pengfei. Study on Travel Time Reliability Considering Route Travel Time Boundary [J]. Journal of South China University of Technology (Natural Science Edition), 2019, 47(6): 127-135.
[7]	YAO Enjian LIU Wenting LIU Shasha YANG Yang. ptimizing Last Train Timetable for Urban Rail Transit Based on Dynamic Accessibility [J]. Journal of South China University of Technology (Natural Science Edition), 2018, 46(1): 58-65.
[8]	BAO Dan-wen LIU Jian-rong GU Jia-yu . Optimization Model of Airport Bus Line Network Reliability and Algorithm Design [J]. Journal of South China University of Technology (Natural Science Edition), 2017, 45(8): 84-91.
[9]	JIN Shan JIN Zhi-gang LIU Yong-lei. A KMP-RBF Fusion Method to Forecast Duty Vehicle's Travel Time [J]. Journal of South China University of Technology (Natural Science Edition), 2017, 45(3): 35-41,47.
[10]	ZHU Guang-Yu DU Chong ZHANG Peng. A Travel Time Forecasting Model Based on Baseline Drift Correction [J]. Journal of South China University of Technology (Natural Science Edition), 2016, 44(8): 131-138.
[11]	YANG Qing-fang WEI Xue-wu LIN Ci-yun LI Zhi-lin LIU Xiang-yu. Reliability Prediction of Travel Time Based on Spatio-Temporal Bayesian Model [J]. Journal of South China University of Technology (Natural Science Edition), 2016, 44(4): 115-122.
[12]	. Estimationof Expressway Section Travel Time Based on Correction Algorithm [J]. Journal of South China University of Technology (Natural Science Edition), 2015, 43(4): 20-27.
[13]	Yan Ying Wang Xiao-Fei . Investigation into Travel Time of Management Unit of Expressway in Disastrous Events [J]. Journal of South China University of Technology (Natural Science Edition), 2015, 43(12): 99-105,113.
[14]	Wang Zhi-peng Luo Xia. Stopping Schedule Optimization of Express/Local Trains in Urban Ｒail Transit [J]. Journal of South China University of Technology (Natural Science Edition), 2015, 43(12): 91-98.
[15]	Zhao Jian- dong Wang Hao Liu Wen- hui. Prediction of Expressway Travel Time Based on Adaptive Interpolation Kalman Filtering [J]. Journal of South China University of Technology (Natural Science Edition), 2014, 42(2): 109-115.